I'd always thought that the difference between an 'air' and other tunes was that an air is a song tune, and consequently played as you would sing it. How that is depends on the song, and I've sometimes been advised that you can't properly interpret many Irish (Gaelic) airs unless you have at least a smattering of Irish so as to get the phrasing right. But generally, the rhythm and phrasing will be freer, and decoration and variation more to be encouraged.